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I have a question regarding sets of finite perimeter. In particular I'm interested to find $$\mu_{E \cap H_t}, \label{1}\tag{1}$$ where $E$ is a set of finite perimeter in a generic open set $\Omega \...

Let $(X,d_X),(Y,d_Y)$ be metric spaces and $X$ is locally-compact and fix a Borel probability measure $\nu$ on $X$. For any Borel-measurable $f:X\rightarrow Y$, let $\mathcal{K}(f,\delta)$ be the set ...